SURFACE AREA

[pappueshwar]

What is the surface area of cuboid C?

1. The length of the diagonal of C is 5.
2. The sum of the sides of C is 10.


OA IS C

[Anurag@Gurome]

What is the surface area of cuboid C?

1. The length of the diagonal of C is 5.
2. The sum of the sides of C is 10.

OA IS C

If l = length, b = width and h = height of cuboid (rectangular prism), then
Surface area of a cuboid = 2(lb + bh + lh)

(1) The length of the diagonal of C is 5.
Length of the diagonal in a cuboid = √(l² + b² + h²)
So, √(l² + b² + h²) = 5 or (l² + b² + h²) = 25, which is definitely NOT sufficient to find the surface area of C.

(2) The sum of the sides of C is 10 implies l + b + h = 10, which is again NOT sufficient to find the surface area of C.

Combining (1) and (2):
(l + b + h)² = (l² + b² + h²) + 2(lb + bh + lh)
(10)² = 25 + 2(lb + bh + lh), solving which we can find the surface area of C; SUFFICIENT.

The correct answer is C.

[pappueshwar]

Anurag,

how did u get this ?

(l + b + h)² = (l² + b² + h²) + 2(lb + bh + lh)

[Anurag@Gurome]

Anurag,

how did u get this ?

(l + b + h)² = (l² + b² + h²) + 2(lb + bh + lh)

I hope you know the identity using 2 variables:
(a + b)² = (a + b)(a + b) = a² + b² + 2ab (you can also do this using FOIL method)

In the same way, for 3 variables,
(a + b + c)² = (a + b + c)(a + b + c) = (a² + b² + c²) + 2(ab + bc + ac)

[ubhanja]

Had this been a cube instead of cuboid, answer D would have been correct I believe.

[Anurag@Gurome]

Had this been a cube instead of cuboid, answer D would have been correct I believe.

Surface area of a cube = 6a², where a is each of the sides of a cube.

(1) The length of the diagonal of cube is 5.
Length of the diagonal in a cube = a√3
So, a√3 = 5
We can find a from the above equation and hence we can find the surface area of cube; SUFFICIENT.

(2) The sum of the sides of C is 10.
3a = 10 implies a = 10/3
So, we can find the surface area of cube; SUFFICIENT.

The correct answer is D in case of a cube.